Finite Group Databasebeta

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C72×Dic195 #50303684

order38220
automorphism?
homologyAbelianization (H1) = C4×C72 · Schur multiplier (H2) = C7

Aliases

direct productC72×Dic195
unambiguous semidirect productC3⋊(C72×Dic65)

Splittings

derived, HallC3×C5×C13 ⋊ C4×C72
HallC3×C5×C72×C13 ⋊ C4
HallC5×C72×C13 ⋊ Dic3
HallC3×C72×C13 ⋊ Dic5
HallC3×C5×C72 ⋊ Dic13
HallC72×C13 ⋊ Dic15
HallC5×C72 ⋊ Dic39
HallC3×C72 ⋊ Dic65
HallC5×C13 ⋊ C72×Dic3
HallC3×C13 ⋊ C72×Dic5
HallC3×C5 ⋊ C72×Dic13
SylowC13 ⋊ C72×Dic15
SylowC5 ⋊ C72×Dic39
SylowC3 ⋊ C72×Dic65

Subgroups

subgroupG/H
center, hypercenterC2×C72D195
commutator, hypocenterC3×C5×C13C4×C72
FrattiniC2C72×D195
Fitting, socle, prime radicalC2×C3×C5×C72×C13C2
cosocleC2×C3×C5×C13C2×C72
LCSG ▷ C3×C5×C13
UCSC1 ◁ C2×C72

240 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 38220

Conjugacy classes & character table

9702 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(38220, 370);